Recently, the collisionless expansion of spherical nanoplasmas has been analyzed with a new ergodic model, clarifying the transition from hydrodynamiclike to Coulomb-explosion regimes, and providing accurate laws for the relevant features of the phenomenon. A complete derivation of the model is presented here. The important issue of the self-consistent initial conditions is addressed by analyzing the initial charging transient due to the electron expansion, in the approximation of immobile ions. A comparison among different kinetic models for the expansion is presented, showing that the ergodic model provides a simplified description, which retains the essential information on the electron distribution, in particular, the energy spectrum. Results are presented for a wide range of initial conditions (determined from a single dimensionless parameter), in excellent agreement with calculations from the exact Vlasov-Poisson theory, thus providing a complete and detailed characterization of all the stages of the expansion.

A model based on a statistical method, as deduced from a path-integral treatment of the Brownian motion proposed by Feynman and Hibbs in 1965, demonstrates to be capable of interpreting the results of delay time measurements in frustrated total internal reflection experiments at an optical and microwave scale. A plausible description of the trajectories followed by the system inside the tunneling region, the air gap between the two dielectric prisms, is given.

An analysis is presented of the phase vortices generated in the far field by an arbitrary arrangement of three monochromatic point sources of complex spherical waves. In contrast with the case of three interfering plane waves, in which an infinitely extended vortex lattice is generated, the spherical sources generate a finite number of phase vortices. Analytical expressions for the vortex core locations are developed and shown to have a convenient representation in a discrete parameter space. Our far-field analysis may be mapped onto the case of a coherently illuminated Young’s interferometer, in which the screen is punctured by three rather than two pinholes.

Multicanonical molecular dynamics (MD) is a powerful technique for sampling conformations on rugged potential surfaces such as protein. However, it is notoriously difficult to estimate the multicanonical temperature effectively. Wang and Landau developed a convenient method for estimating the density of states based on a multicanonical Monte Carlo method. In their method, the density of states is calculated autonomously during a simulation. In this paper, we develop a set of techniques to effectively apply the Wang-Landau method to MD simulations. In the multicanonical MD, the estimation of the derivative of the density of states is critical. In order to estimate it accurately, we devise two original improvements. First, the correction for the density of states is made smooth by using the Gaussian distribution obtained by a short canonical simulation. Second, an approximation is applied to the derivative, which is based on the Gaussian distribution and the multiple weighted histogram technique. A test of this method was performed with small polypeptides, Met-enkephalin and Trp-cage, and it is demonstrated that Wang-Landau MD is consistent with replica exchange MD but can sample much larger conformational space.

We describe here a rigorous and accurate model for the simulation of three-dimensional deformable particles (DPs). The method is very versatile, easily simulating various types of deformable particles such as vesicles, capsules, and biological cells. Each DP is resolved explicitly and advects within the surrounding Newtonian fluid. The DPs have a preferred rest shape (e.g., spherical for vesicles, or biconcave for red blood cells). The model uses a classic hybrid system: an Eulerian approach is used for the Navier-Stokes solver (the lattice Boltzmann method) and a Lagrangian approach for the evolution of the DP mesh. Coupling is accomplished through the lattice Boltzmann velocity field, which transmits force to the membranes of the DPs. The novelty of this method resides in its ability (by design) to simulate a large number of DPs within the bounds of current computational limitations: our simple and efficient approach is to (i) use the lattice Boltzmann method because of its acknowledged efficiency at low Reynolds number and its ease of parallelization, and (ii) model the DP dynamics using a coarse mesh (approximately 500 nodes) and a spring model constraining (if necessary) local area, total area, cell volume, local curvature, and local primary stresses. We show that this approach is comparable to the more common—yet numerically expensive—approach of membrane potential function, through a series of quantitative comparisons. To demonstrate the capabilities of the model, we simulate the flow of 200 densely packed red blood cells—a computationally challenging task. The model is very efficient, requiring of the order of minutes for a single DP in a $50\mathrm{\mu }\mathrm{m}\times 40\mathrm{\mu }\mathrm{m}\times 40\mathrm{\mu }\mathrm{m}$ simulation domain and only hours for 200 DPs in $80\mathrm{\mu }\mathrm{m}\times 30\mathrm{\mu }\mathrm{m}\times 30\mathrm{\mu }\mathrm{m}$. Moreover, the model is highly scalable and efficient compared to other models of blood cells in flow, making it an ideal and unique tool for studying blood flow in microvessels or vesicle or capsule flow (or a mixture of different particles). In addition to directly predicting fluid dynamics in complex suspension in any geometry, the model allows determination of accurate, empirical rules which may improve existing macroscopic, continuum models.

Granular gaseous mixtures under rapid flow conditions are usually modeled as a multicomponent system of smooth inelastic hard disks (two dimensions) or spheres (three dimensions) with constant coefficients of normal restitution ${\alpha }_{ij}$. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard disks or spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. For each collision term $ij$, the model has two parameters: a dimensionless factor ${\beta }_{ij}$ modifying the collision rate of the elastic hard spheres, and the drag coefficient ${\zeta }_{ij}$. Both parameters are determined by requiring that the model reproduces the collisional transfers of momentum and energy of the true inelastic Boltzmann operator, yielding ${\beta }_{ij}=(1+{\alpha }_{ij})∕2$ and ${\zeta }_{ij}\propto 1-{\alpha }_{ij}^2$, where the proportionality constant is a function of the partial densities, velocities, and temperatures of species $i$ and $j$. The Navier-Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman-Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. The discrepancies between both descriptions are seen to be similar to those found for monocomponent gases. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.

The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For nonspherical particles, the distance of closest approach depends on orientation, and its calculation is surprisingly difficult. Although overlap criteria have been developed for use in computer simulations [Vieillard-Baron, J. Chem. Phys. 56, 4729 (1972); Perram and Wertheim, J. Comput. Phys. 58, 409 (1985)], no analytic solutions have been obtained for the distance of closest approach of ellipsoids in three dimensions, or, until now, for ellipses in two dimensions. We have derived an analytic expression for the distance of closest approach of the centers of two arbitrary hard ellipses as a function of their orientation relative to the line joining their centers. We describe our method for solving this problem, illustrate our result, and discuss its usefulness in modeling and simulating systems of anisometric particles such as liquid crystals.

We investigate polymer translocation through a nanopore under a pulling force using Langevin dynamics simulations. We concentrate on the influence of the chain length $N$ and the pulling force $F$ on the translocation time $\tau$. The distribution of $\tau$ is symmetric and narrow for strong $F$. We find that $\tau \sim N^2$ and translocation velocity $v\sim N^{-1}$ for both moderate and strong $F$. For infinitely wide pores, three regimes are observed for $\tau$ as a function of $F$. With increasing $F$, $\tau$ is independent of $F$ for weak $F$, and then $\tau \sim F^{-2+{\nu }^{-1}}$ for moderate $F$, where $\nu$ is the Flory exponent, which finally crosses over to $\tau \sim F^{-1}$ for strong force. For narrow pores, even for moderate force $\tau \sim F^{-1}$. Finally, the waiting time, for monomer $s$ and monomer $s+1$ to exit the pore, has a maximum for $s$ close to the end of the chain, in contrast to the case where the polymer is driven by an external force within the pore.

We introduce a discrete element simulation for the hydraulic fracture process in a petroleum well which takes into account the elastic behavior of the rock and the Mohr-Coulomb fracture criterium. The rock is modeled as an array of Voronoi polygons joined by elastic beams, which are submitted to tectonical stresses and the hydrostatic pressure of the fracturing fluid. The fluid pressure is treated like that of a hydraulic column. The simulation reproduces well the time and dimensions of real fracture processes. We also include an analysis of the fracturing fluid loss due to the permeability of the rock which is useful in an efficiency analysis of the treatment. The model is a first step for future applications in the petroleum industry.

Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these coherent states, calculate the fraction of time the structures appear in the flow, and present a Markov model for the transition between the structures. The fraction of states that show vortical structures exceeds 24% for a Reynolds number of about $\mathrm{Re}=2200$, and it decreases to about 20% for $\mathrm{Re}=2500$. The Markov model for the transition between these states is in good agreement with the observed fraction of states, and in reasonable agreement with the prediction for their persistence. It provides insight into dominant qualitative changes of the flow when increasing the Reynolds number.

The finite-length effect of a resonant nonlinear photonic crystal on the propagation dynamics of gap solitons is theoretically studied. This effect results in a dissipation and deceleration of the moving gap solitons such that the propagation dynamics is essentially different from that on an infinite domain. Due to this effect, two slow counterpropagating solitons can collide into a nonmoving breatherlike bound state, even under many realistic excitation circumstances.

In a causally dispersive medium the signal arrival appears in the dynamical field evolution as an increase in the field amplitude from that of the precursor fields to that of the steady-state signal. The interrelated effects of phase dispersion and frequency dependent attenuation and/or amplification alter the pulse in such a fundamental way that results in the appearance of precursor fields. Although superluminal group velocities have been found in various dispersive media, the pulse “front” and associated precursors will never travel faster than $c$, and hence these are the vehicles through which relativistic causality is preserved. While many rigorous studies of wave propagation and associated abnormal group velocities in passive Lorentzian media have been performed, the corresponding problem in active media has remained theoretically unexplored. This problem is addressed in the present paper, by employing the steepest descent method for the determination of the response of an active Lorentzian medium to a step modulated pulse. The steepest descent method provides a detailed description of the propagation of the pulse inside the dispersive medium in the time domain. Moreover, the evolution of the saddle points illuminates the relation between the medium parameters and the temporal evolution of the propagating pulse within the medium. Hence, useful physical insights are obtained and the interesting differences between the passive and active case are deduced.

Several different interpolation schemes have been proposed for improving the accuracy of lattice Boltzmann simulations in the vicinity of a solid boundary. However, these methods require at least two or three fluid nodes between nearby solid surfaces, a condition that may not be fulfilled in dense suspensions or porous media for example. Here we propose an interpolation of the equilibrium distribution, which leads to a velocity field that is both second-order accurate in space and independent of viscosity. The equilibrium interpolation rule infers population densities on the boundary itself to reduce the span of nodes needed for interpolation; it requires a minimum of one grid spacing between the nodes. By contrast, the linear interpolation rule requires two fluid nodes in the gap and leads to a viscosity-dependent slip velocity, while the multireflection rule is viscosity independent but requires a minimum of three fluid nodes.

The correlations between the response of a random walker to an external driving field $F$ switched on at time $t_a$, with the particle’s fluctuations in the aging period $(0,t_a)$ are investigated. Using the continuous time random walk and the quenched trap model, it is shown that these correlations remain finite even in the asymptotic limit $t_a\to \infty$. Linear response theory gives a relation between the correlations, the fractional diffusion coefficient, and the field $F$, thus generalizing the Einstein relation. In systems which exhibit aging, fluctuations in the aging period can be used to statistically predict the nonidentical response of particles to an external field.

Electric induced dipoles of nanocolloids the size of the Debye length are shown to be one order stronger than predicted by the classical Maxwell-Wagner theory and its extensions. The difference is attributed to normal ion migration within the diffuse layer, and adsorption onto the Stern layer at the poles. The characteristic relaxation frequency (the crossover frequency for dielectrophoresis) is shown to be inversely proportional to the $RC$ time of the diffuse layer capacitance and resistance, and has an anomalous $-1$ scaling with respect to the product of the Debye length and the particle size.

We consider a single Rouse polymer chain in two dimensions in the presence of a transverse shear flow along the $x$ direction and calculate the persistence probability $P_0\left(t\right)$ that the $x$ coordinate of a bead in the bulk of the chain does not return to its initial position up to time $t$. We show that the persistence decays at late times as a power law $P_0\left(t\right)\sim t^{-\theta }$ with a nontrivial exponent $\theta$. The analytical estimate of $\theta =0.359\dots$ obtained using an independent interval approximation is in excellent agreement with the numerical value $\theta \approx 0.360\pm 0.001$.

Carpenter et al. [Phys. Rev. E 61, 532 (2000)] succeeded in determining a single universal model, called the P1 model, that could describe the ellipsometric critical adsorption data from the liquid-vapor interface of four different critical binary liquid mixtures near their critical demixing temperatures. The P1 model also recently has been used to describe neutron reflectometry data from a critical liquid mixture/crystalline quartz interface. However, in another recent study, the P1 model failed to simultaneously describe x-ray reflectometry and ellipsometry data from the liquid-vapor surface of the critical mixture $n$-dodecane $+$ tetrabromoethane (DT). In this paper, we resolve this discrepancy between x-ray and ellipsometric data for the DT system. At large length scales (far from the interface) the local concentration is described by the P1 model in order to correctly reproduce the temperature dependence of the ellipsometric data. Close to the interface, however, the molecular structure must be correctly accounted for in order to quantitatively explain the x-ray data. An important conclusion that arises from this study is that neutron or x-ray reflectometry is most sensitive to short-range interfacial structure, but may provide misleading information about long-range interfacial structure. Ellipsometry provides a more accurate measure of this long-range interfacial structure. Complex interfacial structures, possessing both short- and long-range structure, are therefore best studied using multiple techniques.

We use a two-dimensional random-force model to investigate the velocity distributions in driven granular media. In general, the shape of the distribution is found to depend on the degree of dissipation and the packing fraction but, in highly dissipative systems, the velocity distributions have tails close to exponential. We show that these arise from the dynamics of single particles traveling in dilute regions and influenced predominantly by the random force. A self-consistent kinetic theory is developed to describe this behavior.

Understanding how opinions spread through a community or how consensus emerges in noisy environments can have a significant impact on our comprehension of social relations among individuals. In this work a model for the dynamics of opinion formation is introduced. The model is based on a nonlinear interaction between opinion vectors of agents plus a stochastic variable to account for the effect of noise in the way the agents communicate. The dynamics presented is able to generate rich dynamical patterns of interacting groups or clusters of agents with the same opinion without a leader or centralized control. Our results show that by increasing the intensity of noise, the system goes from consensus to a disordered state. Depending on the number of competing opinions and the details of the network of interactions, the system displays a first- or a second-order transition. We compare the behavior of different topologies of interactions: one-dimensional chains, and annealed and complex networks.